the photoresist on the blank grids and then hydro form them. ... the screen and accelerator be simultaneously hydro ... Hughes Research Labs., Malibu, Calif. 6.
NASA
t..
TECHN ICAL MEMORANDUM
vO I
X
5) The cold girdtogrid spacings measurements are estimated to be accurate within 0.05 mm. Discharage Chamber Performance Energy per beam ion versus utilization.  Two methods of obtaining the variation of the energy per beam ion, Ep as a function of propellant utilization efficiency, ru, have been used. The first method used a slow pointbypoint measurement of r)u in which the beam current and discharge voltage were held fixed. The discharge current and flow rates were varied to produce the curve. The second and faster method required a r) measurement at a nominal .operating point. Then, while the vaporizer heater powers were held constant, the discharge voltage and current were changed to vary the beam current, thereby changing the Ej and rj . The two methods yielded different curves because the beam current was constant in one case and not in the other. In the second case, the discharge voltage may have increased to a value at which the degree of doubly ionized mercury atoms was not negligible. Also, the temperatures of the mercury vaporizers could have changed due to thermal feedback from the discharge chamber. Mercury flow rate measurements.  The mercury flow rates were obtained by measuring a drop in the height of a mercury column inside of a calibrated flow tube during a known time interval. Mercury flow rates were repeatable to 1 percent and were estimated to be accurate within 2 percent. Theoretical Analysis Grid Deflection A brief calculation was made of the deflection of dished grids under thermal loading. Because data presented herein were obtained with grids
without intermediate grid supports, the analysis of deflection will be for grids supported only on the edges. It was assumed that the shapes of the screen and accelerator grids were spherical before operation. It was assumed that the radii of curvature of both grids were equal. Figure 2 shows the model used for the calculations.
give expansions as if the entire ring or grid were at the average temperatures. It can be shown to a good approximation that the new values of maximum angle of dish Tmax and radius of curvature R_o are: 1/2 .
Present tests indicate that during operation the center of the screen grid heats up to between 350 to 550 C and the center of the accelerator grid to a somewhat lower temperature. Thermal gradients of 350 C could exist between the center of the , grids and the ring support. Because the supports are cooler than the grids, the grids deflect by an amount, At, which depends on the average temperature of the grid and the temperature of the ring support. It was assumed that the new shapes, shown by the dotted line on Fig. 2, were also spherical. The screen grid was the hotter of the two grids and underwent the most deflection. The intent of the following calculation is to determine the gridtogrid spacing variation for various geometries and operating conditions. The variation of spacing is defined as the net difference between the deflection of each grid during operation. Figure 4 shows the grids dished concave, and in this case the gridtogrid spacing increased during operation. When the grids were dished convex the grids became closer together under thermal loading.
(7) (8)
sin
The maximum value of the angle p
max
'max
\'max
p is :
i \ 'maxj
O)
where (10)
Ar'max
The axial distance between the centers of curvature of the grid before and during operation is: R sin
Az =
1 sin V(rmax + Ar' '
(11)
In general From Fig. 2 it can be seen that the deflection of a single grid, At, can be obtained from the equation: Az sin
(1)
The known dimensions are the dish depth, h', and a half chord length, R^.. The grid has a radius of curvature, Rg, given by: :
+ h' 8
The maximum angle of dish tial arc length of the grid S' are: = sin I —
31
(2)
2h' and the
ini
(3)
= 2wRg
When the grid and grid mounting ring heat up, both expand and the dished area assumes a new half chord length and arc length which are given by: RP = 4(1
(5)
S = S' (1 +
(6)
where Oj. and a are the coefficients of expansion of the mounting ring and grid material, respectively. The temperature increases of the ring and grid are ATr and AT and are both average values. Average temperature values are used to
(12) and sin r = R^~ g
(13)
Substitution of Eqs. (2), (11), (12), and (13) into Eq. (l) gives the deflection of the grid during operation, At, at any point P. At is. meas ured along an extension of the initial radius of curvature to P. Equation (1) can be used to determine the deflection of a particular grid configuration. The gridtogrid spacing variation can be calculated by substituting values of ATr and AT for both the screen and accelerator into Eq. (5) and (e). Substitution of various values of h' into Eq. (2) can show the effect of various values of dish depth. The results of this calculation are presented later. Thrust losses from hole misalinement.  The present technique of dishing grids with identical hole patterns leads to a grid hole misalinement which is a function of r Figure 6(a) is a section view of the grids after dishing and stress relieving. Figure 6(b) shows the same set of grids during operation with the grids mounted convex. Figure 6(b) also shows that there is a grid hole misalinement (maximum at the outer holes) caused by the gridtogrid spacing separation. The current grid at element thruster axis is is deflected by
density extracted at the screen dA and at an angle y from the defined as j(r). Each beamlet r due to the shape of the grid.
The grid hole misalinement leads to an additional beam deflection, A, which is a function of r The following section will present calculations to determine the effect of dishing on the thrust to beam power ratio. This is a measure of the thrust loss due to ion beam divergence from the grid set as assembled. It is beyond the scope of this report to determine analytically beam deflections due to grid distortions during operation. Such additional beam deflections may add or subtract to the thrust losses caused by the basic grid geometry. The total axial thrust and beam power of a dished grid can be calculated by:
t* d r I 7
m
Jo
/ 2q Jo
Perveance of dished grids.  The following form of Child's law was used by Kerslake to calculate ion beam currents extracted by the grid systems of ion engines.( 8 >1°) I. ^2. (AV)3/2 = 0.386XLO"8 ^£ (AV) 2m »2 ' ,2
3/2
(20)
j(r) cos (r + A) sin
t/o
(14)
2/»2« r P.Sd B
Some geometric properties of the grid sets tested are listed in Table II. Grids with minimum hole diameters of 1.2 and 1.9 mm were tested. The cold (room temperature) gridtogrid spacing was varied from 0.30 mm to 0.86 mm. The grids were operated convex and concave.
/»r de/ jO(T) Jo
sin
(15)
From Ref. 11, it is shown to a good approximation over a large range of grid designs that I A = C]_ Ci ~ ^~sin
(16)
Equations (14), (15), and (16) can be used to calculate the thrust to beam power ratios of dished grids. Two different forms of j(r) were assumed. For the first calculation it was assumed that j(r) was constant. Then it was assumed that
d(r) = O(P) cos
(17)
The authors believe that the actual variation of j(r) is between these two expressions. In the argument of the cosine in Eq. (14), the small angle approximation was made, i.e., Cgr
(18)
Substitution of Eq. (18) and the two values of ion current density into Eqs. (14) and (15) allows the thrust to beam power ratios to be evaluated in closed integral form. The value of the thrust to beam power ratio for an ideal grid with no divergence loss is; ideal = 2/v
(19)
To normalize the divergence thrust loss, the values of thrust to beam power ratios calculated from Eqs. (14) and (15) are multiplied by the product v/2. Results and Discussion Operation of Dished TwoGrid Accelerator Systems Dished grids have been fabricated and operated on a 30cm thruster over a large range of test conditions. The grid voltages, spacings, dish direction, and hole diameters have been varied and found to affect the thruster performance. An attempt will be made to separate and discuss these parameters and their effects.
For a constant diode configuration, the factors preceding (AV)3/2 have been given the name "perveance." The grid sets of Table II were evaluated by determining the minimum acceptable total accelerating voltage at several beam currents as described in the Apparatus and Procedure section. Figure 7 is a plot of the knee voltages at the corresponding beam currents for the six grid sets tested. The shaded portion of Fig. 7 shows the region of composite grid operation from Refs. (4) and (5). Because an of the dished grids had approximately the same effective open area, the primary cause for the different positions was the different ion accelerating distance of each grid set. Figure 7 shows that the beam current extracted by each grid set increased with voltage but at a power greater than the threehalves predicted by Child's law. This could occur if the plasma density profile varied as the thruster conditions were changed at higher beam currents. The actual beam currents shown in Fig. 7 are only 20 to 60 percent of the ideal beam current predicted by Eq. (20) when the sum of the hot grid spacing and the screen grid thickness is used for the ion acceleration distance. The experimental perveance is probably less than ideal because: (1) The plasma density profile is not uniform across the grid. (2) At the grid spacing to hole diameter ratios used herein, the grid aperture effect'^) predicts reductions of the ideal beam current between 35 and 55 percent. The data presented in Fig. 7 show that a thruster with dished grid meets the performance requirements of near term, high thrust, low specific impulse missions. Gridtogrid spacing.  The perveance for the grid sets of tests 2 and 4 are shown in Table II and Fig. 7. For test 2 the grids were mounted convex and the cold grid spacing was 0.86 mm. For test 4 the grids were mounted concave with a spacing of 0.33 mm. When operated, the perveance of grids of test 2 was identical to that of test 4. As explained earlier, the spacing of the grids during operation decreased for test 2 and increased for test 4. The change in spacing during operation for the grids of tests 2 and 4 was estimated by assuming that:
(1) Two sets of grids having the same extraction hole geometry and perveance must also have the same effective ion accelerating distance.
a dish as possible. On the other hand, the thrust losses increase as the dish depth increases. This thrust loss will be discussed later in the text.
(2) Under identical thermal loading, the grid deflection is independent of the grid dish direction.
Ratio of nettototal voltage.  At a fixed total voltage and beam current, the specific impulse of the thruster can be varied, within limits, by changing the ratio of the nettototal voltage, R.
The change in spacing was expected to be about onehalf the difference of the cold spacing, or 0.26 mm. This gave a hot gridtogrid spacing of 0.60 mm for each test. Figure 8 is a plot of the beam currents from Fig. 7 at a constant total voltage of 1000 volts as a function of t, the ion accelerating distance. The ion accelerating distance was calculated as the sum of the cold spacing, the 0.38 mm screen grid thickness, and the positive or negative 0.26 mm estimated change in spacing during operation.
Figure 10 is a plot of the ratio of the accelerator impingement current to the beam current, as a function of the total voltage at four values of R, for the grid set of test 2. It shows that the knee voltage changed only 90 volts for a variation of R from 0.67 to 0.40. At the lowest value of R, 0.33, the knee voltage became more difficult to determine.
A noticeable effect of R variation is that the base level accelerator impingement current increased with decreasing R. This is also shown in Figure 8 shows that the beam current increased Fig. 11, which is a plot of the ratio of impinge. as I was decreased. The slope of the line drawn ment current to beam current for the grids of test 2 through the data for the grids was 1.9 mm diameter as a function of R. The beam current was varied holes is 1.3 rather than 2 as expected from from 1.5 to 2.5 amperes and the total voltage was Eq. (20). Again, probable reasons for the reduced varied from 1300 to 1700 volts. The propellant experimental beam currents are the nonuniform plasutilization efficiency was greater than 0.85 and ma density profile and the grid aperture effect. the total voltage was always greater than the knee value. In general, the ratio of impingement current In test 2 the discharge power was varied from to beam current increased as R decreased, thereby 200 to 500 watts at a beam current of 1.0 amperes. increasing the accelerator power loss and decreasing The knee value of total voltage was not changed by the expected accelerator grid lifetime. The data this variation of thermal loading. were grouped in a single band showing a primary dependence on only R and not beam current or total The grid temperature was probably proportional voltage. The increase in accelerator current as R to the fourth root of the discharge power. If this was decreased could have been due to either an inwas the case, the spacing probably did not change crease in the amount of direct impingement or an inmuch during operation and most of the change in crease in the charge exchange current. The distance grid spacing probably occurred when the discharge for charge exchange to occur increases as R is was first turned on. Figure 9 shows the calculated decreased.(I3) Attempts to operate the grids at variation of gridtogrid spacing of a grid set dur values of R greater than about 0.75 resulted in an ing operation for several values of dish depth and accelerator voltage which was too small in magnitude an initial value of Rl of 15 cm. The temperature to prevent electron backstreaming. At R ratios increases, ££Tro and &TrA, of the screen and acless than 0.5 the ion impingement increased above celerator mounting rings were assumed equal to 1.0 percent of the beam current. This sensitivity 170 C. The average temperature increase, from room of impingement current to R variation for dished was temperature, of the screen grid, ^as> assumed grids may be a result of the grid hole misalinement to be 400 C, and the average temperature increase of obtained during the dishing process. This problem the accelerator grid, £®^, was assumed to be 300 C. might be minimized if the grids were dished such that no hole misalinement occurred on the grids. The gridtogrid spacing variation is maximum at the center of the grid and falls to zero at the Grid hole diameter and etch.  Grids with hole edge of the grid system. For the conditions assumdiameters of 1.2 and 1.9 mm were tested. The fraced for Fig. 9, the maximum change in spacing for a tion open area of all grids tested was about 0.50. 2.54 cm dish, which was used for «n performance Preliminary results, shown in Figs. 7 and 8, have data presented herein, was about 0.36 mm. When an indicated a loss in the grid extraction capability average temperature increase of 350 C (instead of when the hole size was decreased from 1.9 to 1.2 mm 300 C) for, the accelerator grid was assumed, the for a constant spacing. Further testing would be maximum variation in gridtogrid spacing was required to determine the optimum hole diameter for 0.18 mm. The 0.36 and 0.18 mm maximum variations in closely spaced 30cm diameter grids. the calculated gridtogrid spacing are in approximate agreement with the 0.26 mm average variation In order to determine the effect, if any, of estimate obtained from the grid operation. the grid etch on grid perveance, tests 2 and 5 were conducted. In test 2, both grids had a 5050 etch The change in spacing is a strong function" while in test 5, the screen grid had a 9010 etch of the initial dish depth. For example, the calcuand the accelerator had a 5050 etch. The grids of lated value of the maximum change in spacing detests 2 and 5 had equal cold spacings of 0.86 mm creased by about a factor of 2.5 as the chosen iniand were dished convex. As shown in Fig. 8 and tial dish depth increased from 1.27 to 3.81 cm. Table II, the perveance was identical for both iyi.d sets. The data of Fig. 9 indicate that to minimize the gridtogrici spacing variation during operation, Electron backstrearainK.  During the operation it is desirable to fabricate the grids with as deep of dished grids, the electron backstreaming limit of
the accelerator voltage was. found to be a function of the beam current, accelerator grid hole diameter, net accelerating voltage, E, and grid spacing. Figure 12 shows the effect of the value of beam current and the accelerator grid hole diameter on the electron backstreaming limit. The absolute value of the accelerator voltage backstreaming limit increases approximately linearly with beam current. The scatter in the data for grids with 1.9 mm diameter holes is largely due to the wide range of net accelerating voltages used—from 300 to 1200 volts. The backstreaming limit for the grids with 1.2 mm diameter holes was roughly 40 percent of that required for the larger 1.9 mm holes. The Effects of Dished Grids on Discharge Chamber Performance References 3, 4, 5, 13, and 14 have shown that the ion extraction system affects the thruster discharge chamber performance. This section presents similar results showing the effect of grid system parameters such as grid type, voltages, and dish direction on the discharge chamber performance. Grid type.  Figure 13 is a plot of the discharge energy per beam ion, Er, as a function of the propellant utilization efficiency, n, for 30cm thrusters with several different accelerator grid systems. The Ej of the thruster with the present dished grids was about 325 at a r^ of 90 percent whereas the E with composite grids was about 170.(4;5) This increase in Ej was probably due to the decrease in the fraction open area of the dished grids (51 percent) from the effective value for composite grids (estimated to be >90 percent!4)). The thruster on which the dished grids were tested was also optimized for composite grids and it is possible that some improvement in EI could have been realized with appropriate discharge chamber modifications. Total voltage.  In general, as the total accelerating voltage was lowered, the beam current would decrease slightly. As mentioned in the Apparatus and Procedure, the discharge current was increased to maintain a constant beam current. Thus, as the total voltage was decreased, the Ej had to be increased to maintain a constant T^. This effect is shown in Fig. 14. At a beam current of 1.5 A, the total voltage was lowered from 1600 to 1400 volts at a constant R. At an r^ of 86 percent Ej increased by about 25. This degradation was probably the result of the plasma sheath at the screen grid moving away from the discharge chamber as the total voltage was lowered and creating a smaller effective grid open area. (13)
ated at a total voltage 450 volts less than test 3. This effect was probably due to the decreased hot spacing for the convex grids of test 2 and the increased hot spacing for the concave grids of test 3. Reference 13 has also shown that E, increased as the grid spacing was increased. Thrust Losses Thrust Losses from Hole Misalinement The losses in thrust, calculated from Eqs. (14) and (15) arising from grid hole misalinement clue to the separation of dished grid are presented in Fig. 16. Figure 16 shows the normalized thrust to beam power ratio plotted as a function of grid dish depth for a 30cm diameter thruster. As explained in Ref. 11, the thrust loss is a function of the ratio of the cold grid spacing to hole diameter ratio tg/Ds. Therefore, two values of tg/Dg, similar to those used experimental 1 y, are shown. The case of no misalinement is also shown. In this case, the grids are assumed to be fabricated in such a fashion as to ail low the ions to be ejected normal to the grid surface and the thrust loss is due only to the spherical shape of the grid surface. For convenience it will be assumed that the actual thrust loss is midway between that predicted by use of the two different assumed ion current density profiles. Figure 16 shows that the thrust losses due to beam divergence increase with both the grid dish depth and the tg/Dg ratio. The. divergence loss for the case of no misalinement varies from about 0.5 to 5 percent as the dish depth increases from 1.27 to 3.81 cm. For the case of misalined grid holes, the thrust loss increases strongly with the lD s/Ds ratio. A dish depth of 2.54 cm and t /Ds ratios .of 0.23 and 0.6 were used for the experimental data of this paper. For these grid geometries the estimated thrust losses were between 4 and 8 percent. Methods of .Reducing Thrust Losses The inherent thrust losses of present dished grids can be reduced if the geometry of the dished grids is such that the hole misalinement is lessened or even misalined such that the beamlet deflection, A, corrects for the angle f
Two techniques which may help reduce or change the sign of A are hole pattern compensation and/ or dishing with a spacer between the screen and accelerator grid. Hole pattern compensation corrects the misalinement by using a different hole centertocenter spacing for the screen grid than for the accelerator grid. For grids dished concave Direction of grid dish.  Figure 15 is a plot the screen grid hole centertocenter spacing would of EI versus r^ for tests Z and 3 of Table II be greater than that of the accelerator. For grids where the cold grid spacings were identical but the dished convex, the screen grid hole centertodish directions were opposite. The data were obcenter spacing would be less than that of the acceltained at a beam current of 2.0 amperes.. The total erator grid. Grids fabricated with these two accelerating voltages necessary to operate about slightly different centertocenter spacings' would 200 volts above the knee were 1350 and 1800 volts be hydroformed in the normal simultaneous manner. for tests 2 and 3, respectively. The angle A could also be reduced by dishing the grids with a hydroformable spacer sheet between As shown previously, operation at a lower total them and bonded to them. Negative values of A voltage degraded discharge chamber performance. could be achieved by using even thicker spacer However, it is shown in Fig. 15 that at an Ej of sheets. The stress relieving would also be done 350, the r^ of test 2 was 12 percent higher than with the spacer sheet in place. test 3. This occurred even though test 2 was oper
Methods of Increasing the Dish Depth The dished grid data presented in this paper is representative of approximately 50 percent open area screen grids. Substantial performance gains could be made by operation with higher open area screen grids. Attempts to hydroform higher open area grids by the technique presented earlier in this paper have resulted in rupture of the central area of the grids. Three new techniques have been tested on scale model grids and indicate ways of increasing the dish depth. The first method of increasing the amount of dish depth tolerable for a given diameter grid is to perform a two step dishing operation. The grids would be hydroformed to near their rupture limit, then stress relieved, and rehydroformed to a dish depth higher than what would be possible by a single hydroforming operation. This technique could, of course, be extended to more than two steps if necessary. A second technique is to force the distribution of elongation of the grid to occur more uniformly over the grid face. During normal single step hydroforming into a female die, the elongation in the central area of the grid is much greater and closer to the rupture limit than near the outer edge of the grid. The elongation of the outer grid region can be forced to be larger than normal by using a two stage dishing operation. The first step consists of hydroforming the grid to a pie pan shape by using a properly shaped die. The second step simply dishes the grids to the desired contour which removes the pie pan shape and allows a deeper dish depth than the single step hydroforming.
Lifetests As of January 1, 1973, the set of grids used in tests 1 through 4 have accumulated 1365 hours of operation, including 700 hours at a beam current of 2.5 amperes. This set of grids has been thermally cycled in 15 separate test segments with no change in the ion extraction capability. The thruster efficiencies (not optimized for minimum fixed power losses or neutralizer flow rate) are listed in Table III. The total thruster efficiency increased from 0.60 to 0.64 and the specific impulse increased from 2620 to 2910 seconds as the beam current was increased from 1.5 to 2.5 amperes. The ideal thrust to power ratio was nearly constant at 46xlO~6 newtons per watt (10~2 ibs/kw). The familiar charge exchange ion erosion pattern on the downstream side of the accelerator was just barely visible. A plasmabridge neutralizer, operating at 50 to 130 equivalent milliamperes, was used for these tests and did not cause any measurable grid erosion. There was a slight erosion pattern on the grid near the neutralizer but the depth was less than the surface roughness. Based on the appearance of the grids after 1365 hours, the time to erode the grids to failure should be well in excess of 10 000 hours. Conclusions
The methods and results of the fabrication and testing of dished grids on a 30cm diameter thruster have been presented. It was found necessary that the screen and accelerator be simultaneously hydroformed and then simultaneously stress relieved to provide matched contours of the two grids. Thus when separated, the spacing was uniform over the The third technique consists of eliminating entire grid surface. When heated to operating temthe catastrophic failure which occurs when a grid perature, the dished design permitted a controlled ruptures. At this point of rupture the minimum thermal expansion of the grids which resulted in webbing areas begin to reduce in cross sectional repeatable high values of grid perveance and thrust area. This further reduces the strength of the densities. These values are equal to or greater grids in that area. As a result, the grid catathan those of the previously tested composites and strophically ruptures (during hydroforming) in the . two grid accelerator systems. Ion beam currents up region where the first cross sectional area reducto 3.0 amperes have been obtained at net acceleration occurs. A method of preventing or retarding tion voltages from 500 to 1500 volts. The beam curthis premature rupture consists of placing a solid rent increased as the total voltage was increased sheet of metal above the grids so that the grids or the grid spacing was decreased but not at the are sandwiched between a stiff solid sheet of metal powers predicted by Child' s law. The accelerator and the rubber sheet used for hydroforming. Local system perveance. and discharge chamber performance weak areas caused by hole irregularities in the improved when a given set of dished grids was grids are then no longer sites of premature rupture mounted convex, as viewed from downstream of the since they are strengthened by the resistance of thruster. hydroforming the stiff solid sheet. One of the grid sets tested has accumulated These three hydroforming technique variations 1365 hours of operation, 700 of which have been at are entirely independent; thus any or all could be a beam current of 2.5 amperes. There has been no used for increasing the amount of dish depth. significant erosion problems with the grids to date. Two additional but yet untested techniques to obtain a deeper dish would hydroform the molybdenum sheets prior to etching the holes. One method would simultaneously hydroform the bare blank grids, stress relieve them and then proceed with the etching process. The other method would be to deposit the photoresist on the blank grids and then hydroform them. The dished sheets would then have the holes chemically etched followed by the simultaneous stress relieving.
From these preliminary results, a closelyspaced, dished accelerator grid system appears to be a solution to the stringent requirements imposed by the near term, high thrust, low specific impulse electric propulsion missions. Appendix  Symbols A0
screen grid open area, cm2
C
a constant screen grid hole diameter, cm
dA
elemental screen grid area, cm2
Superscript:
Ey
discharge energy per beam ion, eV/ion
'
h
grid dish depth, cm
JB
ion beam current, ampere
J
beam current density, amp/cm2
t
ion acceleration distance, grid spacing plus screen grid thickness, cm
prime denoting grid dimensions at room temperature prior to operation
Subscripts:
I
gridtogrid spacing, cm
At
change in ion acceleration distance, cm
m/q
charge to mass ratio, 0.4811x10 for Hg+
r
ion beam power, kW
R
ratio of net to total ion accelerating voltage
B
R
coulomb/kg
accelerator grid
S
screen grid References
1. Bartz, D. R., and Horsewood, J. L., "Characteristics, Capabilities, and Costs of Solar Electric Spacecraft for Planetary Missions," Journal of Spacecraft and Sockets, Vol. 7, No. 12, Dec. 1970, pp. 13791390. 2. Strack, W. C., and Hrach, F.. J., "Early Application of SolarElectric Propulsion of a 1AstronomicalUnit Outofthe Ecliptic Mission," TN D5996, 1970, NASA, Cleveland, Ohio.
radius of curvature of dished grid, cm &
Rr
radius of grid mounting ring or half chord length of dished grid, cm
r
radial distance from beam axis to any point on grid, cm
S
arc length of dished grid, cm
T
thrust of ion engine, newton
K£s
mean temperature increase of grid, °C
fSE
mean temperature increase of mounting ring, °C
&
r
AV
knee value of total accelerating voltage, volts
v
ion velocity, m/sec
Az
change center of curvature of grid before and during operation, cm
a
coefficient of thermal expansion, °C
p
angle between hot and cold radii of curvature at some point on grid, radians
r
angle between thruster axis and any point on grid, radians
^max e it^
max jn um
i '
a^&l6
of
dish, radians
permittivity of free space 8.85x10 coulomb / newtonmeter propellant utilization efficiency
0  aximuthal angle defining position of r, radians X
A
beam deflection angle due to grid hole misalinement, radians
3. Bechtel, R. T., "Performance and Control of a 30CmDiam, LowImpulse, Kaufman Thruster, Journal of Spacecraft and Rockets, Vol. 7", No. 1, Jan. 1970, pp. 2125. 4. Bechtel, R. T., "Component Testing of a 30Centimeter Diameter Electron Bombardment Thruster," Paper 701100, Sept. 1970, AIAA, New York, N.Y. 5. King, H. J. and Poeschel, R. L., "Low Specific Impulse Ion Engine," NASA CR72677, Feb. 1970, Hughes Research Labs., Malibu, Calif. 6. Bechtel, R. T., Banks, B. A., and Reynolds, T. W., "Effect of Facility Backsputtered Material on Performance of GlassCoated Accelerator Grids for Kaufman Thrusters," Paper 71156, Jan. 1971, AIAA, New York, N . Y . 7. Pawlik, E. V., Macie, T., and Ferrera, J., "Electric Propulsion System Performance Eval' uation," Paper 69236, Mai. 1969, AIAA, New York, N.Y. 8. Kerslake, W. R., and Pawlik, E. V., "Additional Studies of Screen and Accelerator Grids for ElectricBombardment Ion Thrustors," TN D1411, 1963, NASA, Cleveland, Ohio. 9. Finke, R. C., Holmes, A. D., and Keller, T. A., "Space Environment Facility for Electric Propulsion Systems Research," TN D2774, 1965, • NASA, Cleveland, Ohio. 10. Kerslake, W. R., "Accelerator Grid Tests on an ElectricBombardment Ion Rocket," TN D1168 1962, NASA, Cleveland, Ohio. 11. Lathem, W. C., and Adam, W. B., "Theoretical Analysis of a GridTranslation Beam Deflection System for a 30on Diameter Kaufman Thruster," TM X67911, 1971, NASA, Cleveland, Ohio.
13. Kerslake, W. R., "ChargeExchange Effects on the Accelerator Impingement of an ElectronBombardment Ion Rocket," TN D1657, 1963, NASA, Cleveland, Ohio. 13. Byers, D. C., "An Experimental Investigation of a HighVoltage ElectronBombardment Ion Thruster," Journal of the Electrochemical Society. Vol. 116, No. 1, Jan. 1969, pp. 917. 14. Bechtel, R. T., "Discharge Chamber Optimization of the SERT II Thruster," Journal of Spacecraft and Rockets, Vol. 5, No. 7, July 1968, pp. 795800.
TABLE I.  DISHED GRID GEOMETRIES
Grid set
Etch
Grid
Minimum Hole diameter,
Equivalent percent open area
Maximum hole diameter (on upstream surface),
Equivalent percent open area
Hole centertocenter spacing,
mm
mm
screen
5050
1.9
51.0
2.0
58.0
accelerator
5050
1.9
51.0
2.0
58.0
screen
9010
1.9
51.0
2.3
73.4
accelerator
5050
1.9
51.0
2.0
58.0
screen
5050
1.2
48.5
1.4
58.9
accelerator
9010
1.2
48.5
1.5
70.3
A
vo
2.54
B
•T
2.54
C
1.71
• Sketch of etches
•
9010
5050
TABLE II.
Test number
 
Table I grid design
Dish direction
Cold grid spacing, mm
 GRID SPACING AND PERFORMANCE
Estimated ion acceleration distance mm
Knee voltage for beam current of; 0.7 A
1.0 A 720 V
1.5 A
2.0 A
2.5 A
830 V 1010 V
1090 V
980
1260
1
A
convex
0.66
0.78
630 V
2
A
convex
0.86
0.98
740
3
A
concave
0.86
1.50
920
A
A. __., _ concave,
0.33
0.97
720
850
980
1160
5
B
convex
0.86
0.98
740
840
980
1140"
12&0
6
C
concave
0.30
0.94
820
960
1330
1500
1040
1290
1220
1140
3.0 A
1420
1550
": T420
F'6796 * TABLE III.  LIFETEST 'PERFORMANCE Total hours at beam current below Table II test number for data i below 'i ], Beam current, < amps !' Net accelerating' voltage, volts ('
25
375
200
700
2
2
1
1
0.7
1.5
2.0
2.5
800
1000
1000
0.004 0.006
0.008
900
Accelerator current, amps !'
0.0015
Accelerator voltage, volts ;'
400
450
500
500
Emission current, amps i
6.0
13.8
20.0
25.0
Discharge voltage, volts ;•
40
40
40
40
Fixed power loss, watts 
87
92
98
103
Total input power, watts 
890
2000
2907
3615
Power efficiency, 1p
0.63
0.68
0.69
0.69
Utilization efficiency,
0.73
0.88
0.90
0.93
Total efficiency, r)T ;
0.46
0.60
0.62
0.64
Spe'cific impulse, sec ;
2520
2620
2820
2910
1u
I
Ideal thrust '• Newton (mlb. ) ' Ideal thrust tp power ratio N/wxlO^
0.041 0.093 0.131 0.164 (73) (58) (21) (9.2) 46
46
45
45
EIGHT 1.59 CM DIAM (5/8 IN.) I MILD STEEL BOLTS
r
r CUPS FOR LIQUID NITROGEN
ALUMINUM EXPANSION CYLINDERS 7
BASE PLATE HIGH PRESSURE FLUID INLET
Figure 1.  Hydroforming apparatus.
THERMALLY LOADED DISHED GRID?
/THERMALLY EXPANDED' / RING MOUNT
R r a r AT r _* ORIGINAL RING MOUNT POSITION
I
w
PRIMED SYMBOLS DENOTE ROOM TEMPERATURE DIMENSIONS UNPRIMED SYMBOLS DENOTE DIMENSIONS UNDER THERMAL LOADING OF NORMAL OPERATION
Figure 2.  Model used for grid deflection calculations.
THRUSTER BODY—
r^ D
M4
C712844 Figure 4.  Dished grid mounted concave on thruster.
2.0
BEAM CURRENT, AMP
1 6
S
KNEE VOLTAGE, kV

8 1.2 ce. o .8
[Ho o o